Genome-wide association studies with hundreds of thousands to millions of SNPs are now feasible. Population admixture and other departures from random mating can confound genetic association studies and produce false positives. Population admixture can also mask true genotype-phenotype associations and produce false negatives. Statistical methods for controlling for the potential confounding effects of population admixture via use of measures of individual ancestry and related techniques is referred to as structured association testing (SAT). Admixed populations also have advantages and can be used to detect genomic regions containing trait-influencing genes (i.e., to find linkage) via regional admixture mapping (RAM). In principle, SAT and RAM allow localization of genomic regions containing trait-influencing genes even in samples of unrelated individuals. We propose developing, evaluating, and applying SAT and RAM methods in the context of genome-wide association studies. We aim to: 1) Assess the measurement properties of individual ancestry and region-specific admixture estimates (which are key inputs into SAT and RAM procedures) and elaborate and evaluate new procedures for assessing the reliability of such estimates in real data;2) Extend a highly flexible general framework we have developed for both SAT and RAM to accommodate measurement error in individual ancestry estimates;3) Combine the general framework with an atheoretical conditioning equations (ACE) approach that does not depend on knowledge of unobservable past events, does not require ancestry informative markers to be specified a priori, is more flexible, and (we hypothesize) will be equally effective for recently admixed populations and more effective for populations with temporally remote and complex admixture histories;4) Offer a method to allow testing for linkage conditional upon association with a polymorphism in a region and, thereby, testing whether that polymorphism appears to account for an observed linkage signal that was detected with RAM;5) Develop and evaluate an entirely novel two-stage approach that has the potential to substantially increase power and efficiency in genome-wide association studies of admixed populations while preserving overall error rates; and 6) Illustrate the methods developed by application to several real datasets.